Yep I hear you, I am often lacking sleep after pulling an all nighter to get my uni work done, go to work next day and take care of child. Damn hard. I find that the best thing is depending on age of children and time of day. Put on a tv show or PS2 for them grab nap on lounge for minimum of ten minutes but not more that an hour. This will give you enough energy to then organise a fun physical activity to do with the kids. The activity must be physical other wise your brain will think you are wanting to sleep and you will be out like a light.

If the nap is not an option, grab the kids and a ball and go for a walk (not car as you might fall asleep while driving).First stop the corner shop, buy them a food that will keep their mouths busy for a long time this way they will not notice that you are unable to listen to them. Next stop, park with a river or water of sorts play with ball eventually let ball get kicked in water then spend the rest of the day trying to get ball out of water without actually entering the water and before you know it they day will be almost over. By the time you get home the kids will be starving feed them, bath them and they will out like a light and so will you.

This is tried and tested and it was also a lot of fun. just don't fall asleep at park and freezing weather could be a problem but hey it's all I got.